Prove E field does not depend on dielectric (capacitors)

[RankWinner]

Homework Statement

"Show that the variation of the potential between the plates of a large parallel plate capacitor remains the same if the air between the plates is replaced by a conductive medium."

Homework Equations

E = σ/ϵ₀ ; C = ϵ₀A/d ' C = Q/V ; E = -dV/dx ; R = ρl/A

The Attempt at a Solution

I've tried a lot of different things, substituting and replacing variables in the equation to try and get ρ to cancel out, but... I honestly have no idea.

 

[Bystander]

Post a couple of the attempts, and maybe someone can point you in the right direction.